Question

The speed of sound at sea level is normally about 340 m/s. A stationary fire alarm has a frequency of 15,000 Hz. An observer running towards the fire alarm hears a frequency of 15,300 Hz. What is the velocity of the observer?

Answer 1

Answer:

The velocity of the observer is 6.8 m/s

Explanation:

Doppler effect equation is given by the formula:

$f'=\frac{v+v_o}{v-v_s} f\\\\where\ f'\ is \ the\ observed \ frequency=15300\ Hz,v_o\ is\ the\ velocity\ of\ the\ observer,\\v_s\ is\ the\ velocity\ of \ source=0,v\ is\ the\ velocity\ of\ sound=340\ m/s\ and\ f\ is\ actual\\frequency=15000\ Hz.\\\\substituting:\\\\15300=15000(\frac{340+v_o}{340} )\\\\340+v_o=346.8\\\\v_o=6.8\ m/s$The velocity of the observer is 6.8 m/s